Guided waves propagating in lossy media are encountered in many problems across different areas of physics such as electromagnetism, elasticity and solid-state physics. They also constitute essential tools in several branches of engineering, aerospace and aircraft engineering, and structural health monitoring for instance. Waveguides also play a central role in many non-destructive evaluation applications. It is of paramount importance to accurately represent the material of the waveguide to obtain reliable and robust information about the guided waves that might be excited in the structure. A reasonable approximation to real solids is the perfectly elastic approach where the frictional losses within the solid are ignored. However, a more realistic approach is to represent the solid as a viscoelastic medium with attenuation for which the dispersion curves of the modes are, in general, different from their elastic counterparts. Existing methods are capable of calculating dispersion curves for attenuated modes but they can be troublesome to find and the solutions are not as reliable as in the perfectly elastic case. In this paper, in order to achieve robust and accurate results for viscoelasticity a spectral collocation method is developed to compute the dispersion curves in generally anisotropic viscoelastic media in flat and cylindrical geometry. Two of the most popular models to account for material damping, Kelvin–Voigt and Hysteretic, are used in various cases of interest. These include orthorhombic and triclinic materials in single- or multi-layered arrays. Also, and due to its importance in industry, a section is devoted to pipes filled with viscous fluids. The results are validated by comparison with those from semi-analytical finite-element simulations.